Algebra Examples

$4 y + 2 (2 y - 4) \leq 2 (2 y + 4)$

Step 1

Simplify $4 y + 2 (2 y - 4)$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$4 y + 2 (2 y) + 2 \cdot - 4 \leq 2 (2 y + 4)$

Step 1.1.2

Multiply $2$ by $2$ .

$4 y + 4 y + 2 \cdot - 4 \leq 2 (2 y + 4)$

Step 1.1.3

Multiply $2$ by $- 4$ .

$4 y + 4 y - 8 \leq 2 (2 y + 4)$

Step 1.2

Add $4 y$ and $4 y$ .

$8 y - 8 \leq 2 (2 y + 4)$

Step 2

Simplify $2 (2 y + 4)$ .

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Step 2.1

Apply the distributive property.

$8 y - 8 \leq 2 (2 y) + 2 \cdot 4$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $2$ by $2$ .

$8 y - 8 \leq 4 y + 2 \cdot 4$

Step 2.2.2

Multiply $2$ by $4$ .

$8 y - 8 \leq 4 y + 8$

Step 3

Move all terms containing $y$ to the left side of the inequality.

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Step 3.1

Subtract $4 y$ from both sides of the inequality.

$8 y - 8 - 4 y \leq 8$

Step 3.2

Subtract $4 y$ from $8 y$ .

$4 y - 8 \leq 8$

Step 4

Move all terms not containing $y$ to the right side of the inequality.

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Step 4.1

Add $8$ to both sides of the inequality.

$4 y \leq 8 + 8$

Step 4.2

Add $8$ and $8$ .

$4 y \leq 16$

Step 5

Divide each term in $4 y \leq 16$ by $4$ and simplify.

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Step 5.1

Divide each term in $4 y \leq 16$ by $4$ .

$\frac{4 y}{4} \leq \frac{16}{4}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $4$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{4 y}{4} \leq \frac{16}{4}$

Step 5.2.1.2

Divide $y$ by $1$ .

$y \leq \frac{16}{4}$

Step 5.3

Simplify the right side.

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Step 5.3.1

Divide $16$ by $4$ .

$y \leq 4$

Step 6

The result can be shown in multiple forms.

Inequality Form:

$y \leq 4$

Interval Notation:

$(- \infty, 4]$